1. Field of the Invention
The present invention relates to measurement systems and methods of evaluating electro-optic (EO) coefficients and thermo-optic (TO) coefficients of optical devices or optical materials, more specifically, to measurement systems and methods of evaluating the electro-optic and thermo-optic coefficients by using interference fringe measurement techniques, wherein those optical characteristics can be precisely measured over a wide wavelength intended without using a complicated measuring equipment.
2. Description of the Related Art
Knowledge of the second-order nonlinear electro-optic coefficients and thermo-optic coefficients of optical materials or optical devices are important in realizing various optical functional devices these days.
The second-order nonlinear electro-optic coefficients are significantly related to optical device performance characteristics of electro-optic modulators, optical deflectors, second harmonic wave generators, wavelength converters, optical switches, optical parametric amplifiers, and quantum entangled optical signal generators, while the thermo-optic coefficients are related to optical device performance characteristics of optical switches, variable filters, variable optical attenuators, and optical modulators.
Thus, measurement of the second-order nonlinear electro-optic coefficients and thermo-optic coefficients of the optical materials or the optical devices is very important because they affect their device performance.
There are a number of conventional measurement methods of evaluating the second-order nonlinear coefficient, such as the Mach-Zehnder interferometer method using a single wavelength light source and a reference optical medium disclosed in K. Onuki, et al., J. Optical Society of America 62 (9), 1030-1032 (1972), and J. A. de Toro, et al., Opt. comm. 154, 23-27 (1998); a method of analyzing an index ellipsoid structure of a reflection-type single beam polarization interferometer of poled polymers disclosed in M. J. Shin, et al., J. Korean Phys. Soc. 31 (1) 99-103 (1997), C. C. Teng & H. T. Man, Appl. Phys. Lett., 56 (18) 1734-1736 (1990), C. J. Novotny, et al., Nano Lett. 8 (4) 1020-1025 (2008), and D. H. Park, et al., Opt. Express 14 (19), 8866-8884 (2006); a method of using interference fringes of transmitted beams after multiple reflection within a Fabry-Perot etalon shaped second-order nonlinear coefficient material disclosed in K. Takizawa and Y. Yokota, Opt. Review 13 (3), 161-167 (1982), and K. Yonekura, et al, Jap. J. Appl. Phys., 47 (7) 5503-5508 (2008); a method of measuring a phase change between two polarization beams caused by the birefringence of a second-order nonlinear material disclosed in Z. Shen, et al., Thin Solid Films 488, 40-44 (2005), H. Adachi, et al. Appl. Phys. Lett., 42 (10) 867-868 (1983), Y. Jeon and H. S. Kang, Opt. Review 14 (6), 373-375 (2007), K. Tada and M. Aoki: Jpn. J. Appl. Phys. 10 (8), 998-1001 (1971), A. Hou, et al., Opt. & Laser Technol. 39, 411-414 (2007), A. Grunnet-Jepsen, et al., J. Opt. Soc. Am. B 12 (5), 921-929 (1995), and K. Li, U.S. patent Ser. No. 10/139,857 (May 6, 2002); a method of using second harmonic wave generation in a second-order nonlinear material disclosed in R. C. Eckardt, et al., IEEE J. Quantum Electron. 26 (5), 922-933 (1990), and I. Shoji, et al., J. Opt. Soc. Am. B 16 (4), 620-624 (1999); a method of measuring a second-order nonlinear coefficient by using spatial distribution of an interferometer output beam of a Mach-Zehnder interferometer composed of bulk-type optics disclosed in H. P. Sardesai, et al., Appl. Opt. 33 (10), 1791-1794 (1994); and a method of measuring an output signal change of an optical waveguide-type Mach-Zehnder interferometer made of a second-order nonlinear material as a function of a applied modulation voltage disclosed in Y. Enami, et al., Nature Photonics, vol. 1, 180-185 (2007) & vol. 1, p. 423 (2007).
The Mach-Zehnder interferometer method using a single wavelength light source and a reference optical medium requires an optical modulator made of a standard and well known second-order nonlinear material, and has disadvantages of limited measurement of the electro-optic coefficient only at a single wavelength and a measurement accuracy limited at the maximum accuracy of the EO coefficient of reference material.
The method of analyzing an index ellipsoid structure of a reflection-type single beam polarization interferometer of poled polymers is a method of obtaining an electro-optic coefficient by preparing one side of a second-order nonlinear optical sample to be a reflective type and the other side to be a transmission type, and adjusting and measuring an angle of a light refracted and reflected within the sample with respect to an irradiated light of a single wavelength. However, in this method the second-order nonlinear optical sample needs to be specially fabricated according to its use, and the measured EO value may have a significant error depending on the angle measurement accuracy and data analysis.
The method of using interference fringes between a light beam directly passing through a Fabry-Perot etalon shaped second-order nonlinear material and transmitted beams after multiple reflections within the material sample uses a method of analyzing frequencies of electric signals generated from an optical detector when it detects modulated signals from the FP etalon shaped second-order nonlinear medium and then comparing their distributions of a Bessel function of the first kind and of the first order and of a Bessel function of the first kind and of the third order. However, this method requires quite complex signal processing steps.
The method of measuring a phase change between two polarization beams caused by the birefringence of a second-order nonlinear material requires adjustment of the polarization state of an input optical signal beam and precise measurement of the polarization states of the output optical signals from the nonlinear material sample, and results in determination of the refractive index of a low accuracy level.
According to the method of using second harmonic wave generation in a second-order nonlinear material, the absolute and a relative values of its second-order nonlinear optical coefficient may be obtained, but it may be difficult to have a phase matching condition for the second harmonic wave generation, and thus it is highly likely that an error may occur.
In the method of measuring the second-order nonlinear coefficient by using spatial distribution of an interferometer output beam of a Mach-Zehnder interferometer composed of bulk-type optics, it is difficult to accurately analyze 2-dimensional interference fringe distribution in a process of determining the nonlinear refractive index, and the same measurement procedures need to be repeated continuously over a desired wavelength range in steps of discrete single wavelength measurement.
Examples of the conventional method of measuring the thermo-optic coefficient include: a method of composing a Mach-Zehnder interferometer with a single wavelength light source disclosed in J. Mangin, P. Strimer and L. Lahlou-Kassi, Meas. Sci. Technol., vol. 4, 826-834 (1993); a method of using an interference fringe of a Fabry-Perot interferometer disclosed in W. J. Tropf and M. E. Thomas, Meas. Johns Hopkins APL Technical Digest, 19 (3), 293-298 (1998); a method of using a change of interference fringes according to rotation of a sample disclosed in S. De Nicola, et al., J. Opt. A: Pure Appl. Opt., 1, 702-705 (1999); a method of using a ring type resonator structure of a sample and a heterodyne optical detection disclosed in S. Chang, et al., Chinese J. Phys. 38 (3-1), 437-442 (2000), and C.-C. Hsu, et al., J. Appl. Phys., vol. 77 (7), 3399-3402 (1995); a method of using a Fizeau interference fringe of a thin sample disclosed in S. S. Bayya, et al., Appl. Opt., vol. 46 (32), 7889-7891 (2007), R. J. Harris, et al., Appl. Opt., vol. 16 (2), 436-438 (1977), and P. A. Williams, et al., Appl. Opt., vol. 35 (19), 3562-3569 (1996); a method of using a heating scheme on a sample and of detecting its TO effect with a prism coupler disclosed in Eun-ji Kim, Young-gyu Lee, Woo-hyuk Jang, Tae-hyung Lee (Samsung Electronics Co., Ltd), Korean Patent No. 10-0322128 (Jan. 14, 2002); a method of measuring waist sizes of a Gaussian optical beam penetrating a liquid or gel-type sample between micro double lenses disposed in L. Huang, et al., CLEO 2004, paper CThII1; and a method of measuring the minimum deviation angle of a penetrating beam through a prism-shaped sample disclosed in D. J. Gettemy, et al., IEEE J. Quantum Electron., 24 (11), 2231-2237 (1988), and B. Zysset, I. Biaggio. and P. Gunter, J. Opt. Soc. Am. B, 9 (3), 380-386 (1992).
In the method of composing a Mach-Zehnder interferometer with a single wavelength light source, Fizeau interference fringes are used together to measure thermal expansion coefficient simultaneously with the TO coefficient, but the measurement scheme is quite complicated and measures the thermo-optic coefficient only at a single wavelength.
In the method of using an interference fringe of a Febry-Perot interferometer an interference fringe spectrum transmitted from a solid etalon-shaped sample is fitted with a Sellmeier equation with suitable coefficients to obtain wavelength dependent refractive indices, and then thermo-optic coefficient is obtained from the refractive index change for various temperatures.
In the method of using a change of interference fringes according to rotation of a sample, a refractive index is calculated from a phase change of the interference fringes caused by rotation of an angle of a thin sample placed on one path of an interferometer. Then, the thermo-optic coefficient is also obtained by obtaining the refractive index change for various temperatures.
The method of using a ring type resonator structure of a sample and a heterodyne optical detection has a drawback because it requires a specially shaped sample so that a light beam propagates in its ring-shaped resonator, and a phase change measuring method with an electrical heterodyne detection scheme.
The method of using Fizeau interference fringes of a thin sample requires thermal expansion coefficient (TEC) measurement by using a conventional commercial TEC measurement method, and determine its thermo-optic coefficient by measuring phase changes of the Fizeau interference fringes formed by reflected beams from the front and rear surfaces of the sample as its temperature is varied. However, this method may be sensitive to vibration on the optical alignment of the bulk optical system under external environment changes.
The method of using a heating scheme on a sample and of detecting its TO effect with a prism coupler is basically based on conventional measurement scheme of the refractive index of an thin film sample, but is packaged with a thermoelectric device to change the temperature of the thin polymer sample.
The method of measuring waist sizes of a Gaussian optical beam penetrating a liquid or gel-type sample between micro double lenses requires use of a liquid or gel type sample only, and also has disadvantages of requiring an inconvenient heating scheme on the sample and of delivering a limited measurement accuracy of the TO coefficient of the sample caused by the measurement accuracy of the waist size of the penetrated optical beam.
The method of measuring the minimum deviation angle of a penetrating beam through a prism-shaped sample has also some drawbacks of requiring preparation of a sample in a prism shape and of limited validity of the method only for the cases that the sample has uniform thermo-optic and thermal expansion coefficients. A refractive index measured by using the method is accurate up to fourth digit after the decimal point, but this method is not accurate enough for the thermo-optic coefficient measurement because the TO coefficients of most materials are on the order of fifth or sixth digits after the decimal point.